=== FILE DESCRIPTION ===
This file contains the 50 sequences and descriptions of the sequences used in evaluation questions 121-170 in samples.jsonl. All 50 evaluation questions using these sequences are also stored separately in the 'obscure-sequences.jsonl' file. The sequences are listed here in the same order as their corresponding evaluation question.

For more information about the sequences herein, visit the On-Line Encyclopedia of Integer Sequences (OEIS) at www.oeis.org.


=== SEQUENCES DESCRIPTION ===
The sequences used in this portion of the evaluation are more obscure, and may relate to more obscure areas of study (e.g., topology, number of queen moves on a chess board, etc.).

For more information about the sequences herein, visit the On-Line Encyclopedia of Integer Sequences (OEIS) at www.oeis.org.


=== SEQUENCES ===
A069754 [Counts transitions between prime and composite to reach the number n.]
{0, 1, 1, 2, 3, 4, 5, 6, 6, 6, 7, 8, 9, 10, 10, 10, 11, 12, 13, 14, 14, 14, 15, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 20, 20, 20, 21, 22, 22, 22, 23, 24, 25, 26, 26, 26, 27, 28, 28, 28, 28, 28, 29, 30, 30, 30, 30, 30, 31, 32, 33, 34, 34, 34, 34, 34, 35, 36, 36, 36, 37, 38, 39}

A035005 [Number of possible queen moves on an n X n chessboard.]
{0, 12, 56, 152, 320, 580, 952, 1456, 2112, 2940, 3960, 5192, 6656, 8372, 10360, 12640, 15232, 18156, 21432, 25080, 29120, 33572, 38456, 43792, 49600, 55900, 62712, 70056, 77952, 86420, 95480, 105152, 115456, 126412, 138040, 150360}

A049366 [Number of Hamiltonian planar graphs with n nodes.]
{0, 0, 1, 3, 7, 36, 221, 2184, 26985, 395877, 6362861, 108791383}

A121941 [Number of unlabeled connected simple graphs with n nodes of degree 4 or less.]
{1, 1, 1, 2, 6, 21, 78, 353, 1929, 12207, 89402, 739335, 6800637, 68531618, 748592936, 8788983173, 110201690911, 1468157196474, 20695559603921, 307590282700915, 4805537369573319, 78710267083015571, 1348394635886684901, 24109112440149231355, 449050443283294835914}

A033549 [Numbers n such that sum of digits of n-th prime equals sum of digits of n.]
{32, 56, 88, 175, 176, 182, 212, 218, 227, 248, 293, 295, 323, 331, 338, 362, 377, 386, 394, 397, 398, 409, 439, 446, 457, 481, 499, 508, 563, 571, 595, 599, 635, 637, 655, 671, 728, 751, 752, 755, 761, 767, 779, 820, 821, 826, 827, 847, 848, 857, 869, 878 }

A002876 [Number of weighted linear spaces of total weight n.]
{1, 2, 4, 8, 16, 36, 85, 239}

A115040 [Minimum largest of a set of n distinct positive integers such that the sum of any pair is a square.]
{3, 30, 3362, 763442}

A030132 [Digital root of Fibonacci(n).]
{0, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9, 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8}

A016069 [Numbers k such that k^2 contains exactly 2 distinct digits.]
{4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 21, 22, 26, 30, 38, 88, 100, 109, 173, 200, 212, 235, 264, 300, 1000, 2000, 3000, 3114, 10000, 20000, 30000, 81619, 100000, 200000, 300000, 1000000, 2000000, 3000000, 10000000, 20000000}

A055670 [a(n) = prime(n) - (-1)^prime(n).]
{1, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 54, 60, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 128, 132, 138, 140, 150, 152, 158, 164, 168, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242, 252, 258, 264, 270, 272, 278, 282, 284}

A007302 [Optimal cost function between two processors at distance n.]
{0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 3, 2, 2, 1, 2, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 2, 2, 1, 2, 2, 3, 2, 3, 3, 3, 2, 3, 3, 4, 3, 4, 3, 3, 2, 3, 3, 4, 3, 4, 3, 3, 2, 3, 3, 3, 2, 3, 2, 2, 1, 2, 2, 3, 2, 3, 3, 3, 2, 3, 3, 4, 3, 4, 3, 3, 2, 3, 3, 4, 3}

A000983 [Size of minimal binary covering code of length n and covering radius 1.]
{1, 2, 2, 4, 7, 12, 16, 32, 62}

A001113 [Decimal expansion of e.]
{2, 7, 1, 8, 2, 8, 1, 8, 2, 8, 4, 5, 9, 0, 4, 5, 2, 3, 5, 3, 6, 0, 2, 8, 7, 4, 7, 1, 3, 5, 2, 6, 6, 2, 4, 9, 7, 7, 5, 7, 2, 4, 7, 0, 9, 3, 6, 9, 9, 9, 5, 9, 5, 7, 4, 9, 6, 6, 9, 6, 7, 6, 2, 7, 7, 2, 4, 0, 7, 6, 6, 3, 0, 3, 5, 3, 5, 4, 7, 5, 9, 4, 5, 7, 1, 3, 8, 2, 1, 7, 8, 5, 2, 5, 1, 6, 6, 4, 2, 7, 4, 2, 7, 4, 6}

A033461 [Number of partitions of n into distinct squares.]
{1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 2, 0, 0, 2, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 0, 2, 3, 1, 1, 4, 3, 0, 1, 2, 2, 1, 0, 1, 4, 3, 0, 2, 4, 2, 1, 3, 2, 1, 2, 3, 3, 2, 1, 3, 6, 3, 0, 2, 5, 3, 0, 1, 3, 3, 3, 4}

A073049 [Least m > 1 such that m^n has m divisors, or 0 if no such m exists.]
{2, 3, 28, 5, 0, 7, 225, 153, 640, 11, 6348, 13, 19474560, 0, 976, 17, 1225, 19, 1521, 81, 0, 23, 343000, 49, 2601, 2133, 3025, 29, 1495296000, 31, 20063232, 4225, 15262600, 4761, 19236456, 37, 25462407801600, 5929, 34633600, 41, 0, 43, 7569, 356445, 8281}

A051336 [Number of arithmetic progressions in {1,2,3,...,n}, including trivial arithmetic progressions of lengths 1 and 2.]
{1, 3, 7, 13, 22, 33, 48, 65, 86, 110, 138, 168, 204, 242, 284, 330, 381, 434, 493, 554, 621, 692, 767, 844, 929, 1017, 1109, 1205, 1307, 1411, 1523, 1637, 1757, 1881, 2009, 2141, 2282, 2425, 2572, 2723, 2882, 3043, 3212, 3383, 3560, 3743, 3930, 4119}

A051628 [Number of digits in decimal expansion of 1/n before the periodic part begins.]
{0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 0, 2, 0, 1, 1, 4, 0, 1, 0, 2, 0, 1, 0, 3, 2, 1, 0, 2, 0, 1, 0, 5, 0, 1, 1, 2, 0, 1, 0, 3, 0, 1, 0, 2, 1, 1, 0, 4, 0, 2, 0, 2, 0, 1, 1, 3, 0, 1, 0, 2, 0, 1, 0, 6, 1, 1, 0, 2, 0, 1, 0, 3, 0, 1, 2, 2, 0, 1, 0, 4, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 0, 2, 0, 1, 1, 5, 0, 1, 0, 2, 0, 1, 0, 3, 1}

A000032 [Lucas numbers beginning at 2: L(n) = L(n-1) + L(n-2), L(0) = 2, L(1) = 1.]
{2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282, 54018521, 87403803}

A048669 [The Jacobsthal function g(n): maximal gap in a list of all the integers relatively prime to n.]
{1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 3, 2, 2, 4, 2, 4, 3, 4, 2, 4, 2, 4, 2, 4, 2, 6, 2, 2, 3, 4, 3, 4, 2, 4, 3, 4, 2, 6, 2, 4, 3, 4, 2, 4, 2, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 6, 2, 4, 3, 2, 3, 6, 2, 4, 3, 6, 2, 4, 2, 4, 3, 4, 3, 6, 2, 4, 2, 4, 2, 6, 3, 4, 3, 4, 2, 6, 3, 4, 3, 4, 3, 4, 2, 4, 3, 4, 2, 6, 2, 4, 5}

A145768 [a(n) = the bitwise XOR of squares of first n natural numbers.]
{0, 1, 5, 12, 28, 5, 33, 16, 80, 1, 101, 28, 140, 37, 225, 0, 256, 33, 357, 12, 412, 37, 449, 976, 400, 993, 325, 924, 140, 965, 65, 896, 1920, 961, 1861, 908, 1692, 965, 1633, 912, 1488, 833, 1445, 668, 1292, 741, 2721, 512, 2816, 609, 2981, 396, 2844, 485}

A000106 [2nd power of rooted tree enumerator; number of linear forests of 2 rooted trees.]
{1, 2, 5, 12, 30, 74, 188, 478, 1235, 3214, 8450, 22370, 59676, 160140, 432237, 1172436, 3194870, 8741442, 24007045, 66154654, 182864692, 506909562, 1408854940, 3925075510, 10959698606, 30665337738, 85967279447, 241433975446, 679192039401, 1913681367936, 5399924120339}

A061417 [Number of permutations up to cyclic rotations; permutation siteswap necklaces.]
{1, 2, 4, 10, 28, 136, 726, 5100, 40362, 363288, 3628810, 39921044, 479001612, 6227066928, 87178295296, 1307675013928, 20922789888016, 355687438476444, 6402373705728018, 121645100594641896, 2432902008177690360}

A046899 [Triangle in which n-th row is {binomial(n+k,k), k=0..n}, n >= 0.]
{1, 1, 2, 1, 3, 6, 1, 4, 10, 20, 1, 5, 15, 35, 70, 1, 6, 21, 56, 126, 252, 1, 7, 28, 84, 210, 462, 924, 1, 8, 36, 120, 330, 792, 1716, 3432, 1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48620, 1, 11, 66, 286, 1001}

A006171 [Number of factorization patterns of polynomials of degree n over integers.]
{1, 1, 3, 5, 11, 17, 34, 52, 94, 145, 244, 370, 603, 899, 1410, 2087, 3186, 4650, 6959, 10040, 14750, 21077, 30479, 43120, 61574, 86308, 121785, 169336, 236475, 326201, 451402, 618135, 848209, 1153733, 1571063, 2123325, 2871419, 3857569, 5182999, 6924303}

A065428 [Numbers k such that no x^2 mod k is prime.]
{1, 2, 3, 4, 5, 8, 12, 15, 16, 24, 28, 40, 48, 56, 60, 72, 88, 112, 120, 168, 232, 240, 280, 312, 408, 520, 760, 840, 1320, 1848}

A003056 [n appears n+1 times. Also the array A(n,k) = n+k (n >= 0, k >= 0) read by antidiagonals. Also inverse of triangular numbers.]
{0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12}

A036364 [Number of free n-ominoes with cell centers determining n-2 space (proper dimension n-2).]
{1, 4, 11, 35, 104, 319, 951, 2862, 8516, 25369, 75167, 222529, 656961, 1937393, 5704426, 16781247, 49320800, 144866243, 425263010, 1247877578, 3660478408, 10734834603, 31475111515, 92273758477, 270486112046, 792836030163, 2323835125879, 6811162237825}

A068148 [Primes in which neighboring digits differ at most by 1.]
{2, 3, 5, 7, 11, 23, 43, 67, 89, 101, 109, 211, 223, 233, 433, 443, 677, 787, 877, 887, 1009, 1109, 1123, 1223, 2111, 2221, 2333, 3221, 3323, 3343, 3433, 4567, 5443, 7789, 7877, 8887, 8999, 9001, 9011, 9887, 9901, 10009, 10099, 10111, 10909, 10987, 12101, 12109}

A030664 [Product of largest prime <= n and smallest prime >= n.]
{1, 1, 4, 9, 15, 25, 35, 49, 77, 77, 77, 121, 143, 169, 221, 221, 221, 289, 323, 361, 437, 437, 437, 529, 667, 667, 667, 667, 667, 841, 899, 961, 1147, 1147, 1147, 1147, 1147, 1369, 1517, 1517, 1517, 1681, 1763, 1849, 2021, 2021, 2021, 2209, 2491, 2491, 2491}

A070939 [Length of binary representation of n.]
{1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6}

A361440 [The number of generators for the monoid of basic unimodal cyclotomic generating functions of degree n.]
{1, 1, 1, 2, 2, 3, 4, 7, 10, 9, 15, 28, 30, 34, 66, 82, 125, 126, 222, 294}

A360706	[a(n) is the least positive number not yet used such that its binary representation has either all or none of its 1-bits in common with the XOR of a(1) to a(n-1).]
{1, 2, 3, 4, 8, 12, 5, 10, 6, 9, 7, 16, 17, 24, 14, 11, 18, 20, 13, 15, 19, 32, 36, 21, 25, 26, 22, 23, 27, 33, 37, 28, 34, 30, 29, 40, 42, 31, 64, 96, 35, 68, 38, 44, 41, 43, 39, 48, 56, 45, 65, 66, 46, 47, 67, 80, 52, 49, 57, 50, 82, 69, 97, 51, 53, 60, 54, 55, 58, 72, 73, 59, 61, 76, 70, 71, 74}

A362477	[E.g.f. satisfies A(x) = exp(x + x^3/6 * A(x)^3).]
{1, 1, 1, 2, 17, 161, 1351, 12391, 153385, 2388905, 40060781, 708351821, 13861042801, 305141790097, 7339275555067, 188198812659131, 5143808931521681, 150713978752271441, 4718460264313196665, 156524510548008965305, 5474266337362911068161}

A362572	[E.g.f. satisfies A(x) = exp(x * A(x)^(x/2)).]
{1, 1, 1, 4, 13, 76, 421, 3361, 26209, 267688, 2689201, 33579811, 412800961, 6103089994, 88754687113, 1517513934301, 25487131948321, 495009722435176, 9430633148123809, 205154208873930763, 4371962638221712801, 105330237499426955926}

A362737	[E.g.f. satisfies A(x) = exp(x^3 + x / A(x)).]
{1, 1, -1, 10, -27, 316, -3725, 63666, -1177687, 25196536, -607345209, 16391726110, -488872392371, 15968546353332, -566886190710853, 21733419523383946, -894910999976666415, 39390009619800983536, -1845602126785662907121, 91714859182521808208694}

A362686	[Binomial(n+p, n) mod n where p=6.]
{0, 0, 0, 2, 2, 0, 1, 3, 1, 8, 1, 0, 1, 8, 9, 5, 1, 10, 1, 10, 15, 12, 1, 15, 6, 14, 1, 8, 1, 12, 1, 9, 12, 18, 8, 10, 1, 20, 27, 19, 1, 36, 1, 12, 10, 24, 1, 45, 1, 36, 18, 14, 1, 28, 12, 15, 39, 30, 1, 48, 1, 32, 1, 17, 14, 12, 1, 18, 24, 50, 1, 19, 1, 38}

A362498	[Number of vertex cuts in the n X n knight graph.]
{0, 0, 256, 48745, 22577890, 50785004331, 447911805432769, 15359769797452095985}

A362546	[Number of odd chordless cycles of length >=5 in the n-Goldberg graph.]
{78, 296, 991, 3828, 15807, 63792}

A362445	[a(n) = (n+1)^4 written in base n.]
{1111111111111111, 1010001, 100111, 21301, 20141, 15041, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641, 14641}

A362699	[Expansion of e.g.f. 1/(1 + LambertW(-x * exp(x^3))).]
{1, 1, 4, 27, 280, 3605, 56376, 1041103, 22188496, 535856553, 14460919120, 431287416131, 14087063106216, 500112706900573, 19174548699128200, 789598137339356535, 34757031591555021856, 1628640121039415039057, 80938770039259919191584}

A360946	[Number of Pythagorean quadruples with inradius n.]
{1, 3, 6, 10, 9, 19, 16, 25, 29, 27, 27, 56, 31, 51, 49, 61, 42, 91, 52, 71, 89, 86, 63, 142, 64, 95, 116, 132, 83, 153, 90, 144, 149, 133, 108, 238, 108, 162, 169, 171, 122, 284, 130, 219, 200, 196, 145, 340, 174, 201, 231, 239, 164, 364, 176, 314, 278, 256, 190, 399, 195, 281, 360, 330}

A362543	[Number of chordless cycles of length >= 4 in the tetrahedral (Johnson) graph.]
{1134, 39651, 5171088, 2660896170, 4613923014804}

A362014	[Number of distinct lines passing through exactly two points in a triangular grid of side n.]
{0, 0, 3, 6, 18, 39, 81, 141, 237, 369, 561, 801, 1119, 1521, 2043, 2667, 3429, 4329, 5415, 6675, 8163, 9879, 11877, 14127, 16695, 19593, 22881, 26523, 30591, 35085, 40089, 45591, 51681, 58359, 65715, 73701, 82389, 91791, 102015, 113007, 124875} 

A362118	[a(n) = (10^(n*(n+1)/2)-1)/9.]
{1, 111, 111111, 1111111111, 111111111111111, 111111111111111111111, 1111111111111111111111111111, 111111111111111111111111111111111111, 111111111111111111111111111111111111111111111, 1111111111111111111111111111111111111111111111111111111, 11111111111111111111111111111111111111111111111111111111111111111}

A361247	[a(n) is the smallest integer k > 2 that satisfies k mod j <= 2 for all integers j in 1..n.]
{3, 3, 3, 4, 5, 6, 30, 42, 56, 72, 792, 792, 1080, 1080, 1080, 30240, 246961, 246961, 636482, 636482, 1360801, 2162162, 2162162, 2162162, 39412802, 39412802, 107881202, 107881202, 3625549202, 3625549202, 3625549202, 170918748001, 170918748001, 170918748001, 170918748001, 170918748001}

A116564 [Ono supersingular invariant power function.]
{0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 6, 6, 12, 12, 20, 12, 20, 30, 20, 30, 42, 42, 42, 56, 56, 72, 56, 72, 90, 110, 110, 110, 132, 132, 132, 156, 182, 182, 210, 182, 240, 210, 240, 240, 272, 306, 342, 306}

A105950	[12 symbol hyper5tetrahedron: three tetrahedra with 5 connections per vertex: a triangle of tetrahedra connected.
{1, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 5, 9, 2, 3, 4, 5, 9, 1, 3, 4, 6, 10, 1, 2, 4, 7, 11, 1, 2, 3, 8, 12, 6, 7, 8, 1, 9, 10, 11, 12, 1, 5, 1, 2, 3, 4, 5, 9, 2, 3, 4, 5, 9, 1, 3, 4, 6, 10, 1, 2, 4, 7, 11, 1, 2, 3, 8, 12, 6, 7, 8, 1, 9, 10, 11, 12, 1, 5, 2, 3, 4, 5, 9, 1, 3, 4, 6, 10, 1, 2, 4, 7, 11, 1, 2, 3, 8, 12}

A106636 [Pair rational approximations of Zeta zeros as an integer sequence.]
{9, 13, 16, 19, 21, 24, 26, 28, 31, 32, 34, 36, 38, 39, 41, 41, 43, 44, 46, 48, 49, 51, 53, 54, 56, 56, 59, 60, 61, 63}

A095737 [Mersenne-like sequence factors of complex real square type 2*Prime[m]^2-n^2-1.]
{2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269}

A116577	[Integer inverse of four parts of Pi by a Prime modulo 12 partition.]
{0, 2900288388, 197346, 5322158, 128736743}